Demand For Offense

Designated Hitters and MLB Attendance

Alexander Cardazzi

Old Dominion University

Zachary Rodriguez

Union College

NBA: Finals Viewership

 

NBA: Finals Viewership

 

NBA: Finals Viewership

 

MLB: World Series Viewership

 

Designated Hitters

In the MLB, like in most team sports, players tend to specialize. This results in pitchers being good at pitching but uniquely terrible at hitting.

\(\rightarrow\) Enter: Designated Hitters

  1. DHs must take the place of pitchers in the batting order.
  2. The DH position first appeared in the AL in 1973.
  3. In 2022, the MLB made the DH position universal (AL + NL).
    • The rule change occured following free agency.
  4. National League teams struggled to adjust to the rule change quickly.
    • NL DH output was substantially lower than that of their AL counterparts.
    • Even still, the DH position was much better than having pitchers bat.

FanGraphs Chart

Research Question

 

How did fans respond to this change in play?

Data Sources

Regular season, game-level data (2013-2022)

  • Attendance, Scores, Records, Location, etc.
  • 20,458 MLB Games

Data Sources

Regular season, game-level data (2013-2022)

  • Attendance, Scores, Records, Location, etc.
  • 20,458 MLB Games
    • Remove 2020 Season
    • Remove Blue Jays in 2021 (travel restrictions)
    • Remove all Houston Astros
    • Remove 28 games with missing beting information

Betting data

  • Oddsshark.com for game-level odds
  • Sportsoddshistory.com for pre- and within-season odds

Summary Statistics

 

Mean St. Dev. Min Max
Attendance (in 1,000s) 28.407 10.961 1.832 59.659
Capacity % 0.650 0.240 0.044 1.580
Home Win 0.535 0.499 0 1
Home Win Prob. 54.053 10.302 20 83.333
Home Score 4.473 3.089 0 25
Away Score 4.357 3.156 0 28
National League 0.534 0.499 0 1
Universal DH 0.111 0.314 0 1
Note: Number of MLB Games = 20,458

Home Team Attendance

 

Methodology

Methodology

Idea 1: Calculate differences in attendance between NL stadiums before & after DHs.

Methodology

Idea 1: Calculate differences in attendance between NL stadiums before & after DHs.

What if attendance is growing/shrinking over time?

Idea 2: Calculate differences in attendance between AL and NL home games in 2022.

Methodology

Idea 1: Calculate differences in attendance between NL stadiums before & after DHs.

What if attendance is growing/shrinking over time?

Idea 2: Calculate differences in attendance between AL and NL home games in 2022.

What if attendance is always higher in NL stadiums?

Idea 3: Calculate differences in the changes in attendance between AL/NL stadiums before/after the DH rule.

Control for initial (pre-DH) levels of attendance across teams.

League wide changes in attendance will be captured in AL stadiums.

Any additional change in NL stadiums is due to the DH rule.

Methodology

Idea 1: Calculate differences in attendance between NL stadiums before & after DHs.

What if attendance is growing/shrinking over time?

Idea 2: Calculate differences in attendance between AL and NL home games in 2022.

What if attendance is always higher in NL stadiums?

Idea 3: Calculate differences in the changes in attendance between AL/NL stadiums before/after the DH rule.

Control for initial (pre-DH) levels of attendance across teams.

League wide changes in attendance will be captured in AL stadiums.

Any additional change in NL stadiums is due to the DH rule.

Methodology

Difference-in-differences:

\[\begin{align} O_{itsomw} &= \delta (\text{NL}_t \times \text{DH}_s) + X_{itsom}\beta + \tau_s + \tau_{to} + \tau_{tm} + \tau_{tw} + \epsilon_{itsomw} \nonumber \end{align}\]

where:

\(O\) is outcome for game \(i\) played by home team \(t\) against opponent \(o\) in season \(s\) in month \(m\) on weekend \(w\).

\(X_{itsom}\) is a vector of controls (# of wins, current winning %, win probability, preseason O/U, pennant odds, Elo rating, 538 rating)
Fixed Effects: Season, team-by-opponent, team-by-month, team-by-weekday, stadium
SEs are either clustered by team-season, or corrected to be made robust to heteroskedasticity

Runs in Home Games by League

 

Runs in Home Games by League

 

Runs in Home Games by League

 

Results – DH on Offense

 

Effect of DH on Offense
O/U Total Score Home Score
NL x DH 0.570 0.422 0.383
(0.059)*** (0.131)** (0.091)***
[0.034]*** [0.214]** [0.145]***
Num.Obs. 20458 20458 20458
R2 0.653 0.148 0.162

Attendance by League

 

Results – DH on Attendance

 

Effect of DH on Attendance
Attendance log(Attendance) Att / Cap Att / Cap (max)
NL x DH 1657.906 0.079 0.037 0.035
(724.193)* (0.035)* (0.018)* (0.017)*
[264.320]*** [0.012]*** [0.006]*** [0.006]***
Num.Obs. 20458 20458 20458 20458
R2 0.795 0.783 0.773 0.775

Results – Event Studies

 

Robustness – Ticket Prices

We do not observe ticket prices!

As demand increases (due to additional offense), prices should also increase.

  • \(\text{Offense} \uparrow \ \text{Price} \uparrow\)

All else equal, increases in price will reduce attendance.

  • \(\text{Price} \uparrow \ \text{Attendance} \downarrow\)

 

Since these correlations are opposite one another, our estimated (positive) coefficient is biased downward. In other words, our estimate is a lower bound.

Robustness – Away Teams

What if NL teams are just better offensively?

  • National League teams used DHs during interleague play prior to the rule change.
  • Therefore, if NL teams are now better offensively, we should see an increase in offense when playing at AL stadiums after the DH rule.
  • While our coefficient estimate is positive, we do not find statistical evidence (two-way or hetero) that there is a difference.

Discussion

The MLB allowed NL teams to use DHs in the 2022 season.

  • Total offense increased by 0.422 (average of 8.83; 4.8%)
  • Attendance increased by 3-8%, depending on the definition.
  • We estimate the “offense elasticity of attendance” to be \(\approx 1\).
    • In other words, increasing offensive output by 1% increases attendance by 1%.
  • Since we do not currently observe ticket prices, this is likely a lower bound.
  • While we observe an increase in attendance, it’s important to note we cannot say much about revenue, let alone profits.

Importantly, this is the first paper to causally quantify fan preferences for offense.

  • So, what should baseball do?

2023 MLB Rule Changes (via MLB.com)

Thanks!


 

alexcardazzi.github.io

(this presentation)

 

sites.google.com/view/zacharyrodriguez

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  • Emotional Cues and Violent Behavior: Unexpected Basketball Losses Increase Incidents of Family Violence

Virginia Wesleyan University